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(b) Suppose that z=x^(2)-2xy^(2) and that x=rcos(theta ),y=rsin(theta ) . i. Sketch a tree diagram representing the dependencies of z on x and y ,
(b) Suppose that
z=x^(2)-2xy^(2)
and that
x=rcos(\\\\theta ),y=rsin(\\\\theta )
.\ i. Sketch a tree diagram representing the dependencies of
z
on
x
and
y
, and
x
and\
y
on
r
and
\\\\theta
.\ ii. Find
(delz)/(delr)
using the tree diagram.\ iii. If
r=3
and
\\\\theta =(\\\\pi )/(6)
, find the value of
(delz)/(delr)
.
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